Simplify to lowest terms. $\dfrac{56}{126}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 56 and 126? $56 = 2\cdot2\cdot2\cdot7$ $126 = 2\cdot3\cdot3\cdot7$ $\mbox{GCD}(56, 126) = 2\cdot7 = 14$ $\dfrac{56}{126} = \dfrac{4 \cdot 14}{ 9\cdot 14}$ $\hphantom{\dfrac{56}{126}} = \dfrac{4}{9} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{56}{126}} = \dfrac{4}{9} \cdot 1$ $\hphantom{\dfrac{56}{126}} = \dfrac{4}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{56}{126}= \dfrac{2\cdot28}{2\cdot63}= \dfrac{2\cdot 7\cdot4}{2\cdot 7\cdot9}= \dfrac{4}{9}$